Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real quadratic subfield (hence A2-4B = m2D for some m).

Class number: [Non-normal] [Cyclic]

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
[25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]
[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]
[73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96]
[97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120]
[121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144]
[145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168]
[169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192]
[193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216]
[217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240]
[241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255] [256] [257] [258] [259] [260] [261] [262] [263] [264]
[265] [266] [267] [268] [269] [270] [271] [272] [273] [274] [275] [276] [277] [278] [279] [280] [281] [282] [283] [284] [285] [286] [287] [288]
[289] [290] [291] [292] [293] [294] [295] [296] [297] [298] [299] [300] [301] [302] [303] [304] [305] [306] [307] [308] [309] [310] [311] [312]
[313] [314] [315] [316] [317] [318] [319] [320] [321] [322] [323] [324] [325] [326] [327] [328] [329] [330] [331] [332] [333] [334] [335] [336]
[337] [338] [339] [340] [341] [342] [343] [344] [345] [346] [347] [348] [349] [350] [351] [352] [353] [354] [355] [356] [357] [358] [359] [360]
[361] [362] [363] [364] [365] [366] [367] [368] [369] [370] [371] [372] [373] [374] [375] [376] [377] [378] [379] [380] [381] [382] [383] [384]
[385] [386] [387] [388] [389] [390] [391] [392] [393] [394] [395] [396] [397] [398] [399] [400] [401] [402] [403] [404] [405] [406] [407] [408]
[409] [410] [411] [412] [413] [414] [415] [416] [417] [418] [419] [420] [421] [422] [423] [424] [425] [426] [427] [428] [429] [430] [431] [432]
[433] [434] [435] [436] [437] [438] [439] [440] [441] [442] [443] [444] [445] [446] [447] [448] [449] [450] [451] [452] [453] [454] [455] [456]
[457] [458] [459] [460] [461] [462] [463] [464] [465] [466] [467] [468] [469] [470] [471] [472] [473] [474] [475] [476] [477] [478] [479] [480]
[481] [482] [483] [484] [485] [486] [487] [488] [489] [490] [491] [492] [493] [494] [495] [496] [497] [498] [499] [500] [501] [502] [503] [504]
[505] [506] [507] [508] [509] [510] [511] [512] [513] [514] [515] [516] [517] [518] [519] [520] [521] [522] [523] [524] [525] [526] [527] [528]
[529] [530] [531] [532] [533] [534] [535] [536] [537] [538] [539] [540] [541] [542] [543] [544] [545] [546] [547] [548] [549] [550] [551] [552]
[553] [554] [555] [556] [557] [558] [559] [560] [561] [562] [563] [564] [565] [566] [567] [568] [569] [570] [571] [572] [573] [574] [575] [576]

Class group C3 x C303 non-normal (D4) quartic CM field invariants: 77 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [61, 3078, 1603337] C3 x C303 ---) [1603337, 1539, 191296] C3 x C3333
2) [229, 3070, 1638081] C3 x C303 ---) [182009, 1535, 179536] C303
3) [229, 2982, 2208425] C3 x C303 48) [88337, 1491, 3664] C3 x C303
4) [229, 418, 35437] C3 x C303 ---) [35437, 209, 2061] C303
5) [257, 2230, 651097] C3 x C303 ---) [651097, 1115, 148032] C303
6) [257, 1418, 49333] C3 x C303 ---) [49333, 709, 113337] C2121
7) [257, 3243, 2165056] C3 x C303 ---) [33829, 1773, 777425] C303
8) [317, 1030, 219577] C3 x C303 ---) [219577, 515, 11412] C3 x C3 x C303
9) [541, 1230, 343601] C3 x C303 59) [343601, 615, 8656] C3 x C303
10) [761, 2167, 1169216] C3 x C303 41) [18269, 3401, 475625] C3 x C303
11) [761, 2479, 874100] C3 x C303 ---) [8741, 2249, 475625] C303
12) [1229, 697, 106397] C3 x C303 ---) [106397, 1394, 60221] C303
13) [2609, 1907, 673700] C3 x C303 28) [6737, 3814, 941849] C3 x C303
14) [2801, 4883, 1136900] C3 x C303 35) [11369, 4355, 3237956] C3 x C303
15) [3221, 282, 6997] C3 x C303 29) [6997, 141, 3221] C3 x C303
16) [3613, 5329, 1173337] C3 x C303 31) [9697, 3379, 2832592] C3 x C303
17) [3769, 1355, 458064] C3 x C303 ---) [3181, 2710, 3769] C3 x C1515
18) [3877, 4053, 11621] C3 x C303 ---) [11621, 5901, 7168573] C2121
19) [4597, 6301, 7386957] C3 x C303 ---) [10133, 3745, 1659517] C303
20) [4597, 3717, 3452873] C3 x C303 ---) [3593, 3835, 3604048] C303
21) [4597, 653, 13513] C3 x C303 ---) [13513, 1306, 372357] C303
22) [4933, 4073, 3938913] C3 x C303 ---) [3617, 3491, 2387572] C303
23) [5261, 2401, 8893] C3 x C303 ---) [8893, 4802, 5729229] C303
24) [5477, 165, 5437] C3 x C303 ---) [5437, 330, 5477] C303
25) [6053, 2629, 927401] C3 x C303 ---) [3209, 4147, 24212] C303
26) [6053, 417, 5641] C3 x C303 ---) [5641, 834, 151325] C303
27) [6053, 3893, 1245089] C3 x C303 ---) [3449, 4127, 387392] C303
28) [6737, 3814, 941849] C3 x C303 13) [2609, 1907, 673700] C3 x C303
29) [6997, 141, 3221] C3 x C303 15) [3221, 282, 6997] C3 x C303
30) [9133, 2953, 2068173] C3 x C303 ---) [2837, 4425, 9133] C303
31) [9697, 3379, 2832592] C3 x C303 16) [3613, 5329, 1173337] C3 x C303
32) [10069, 149, 3033] C3 x C303 ---) [337, 298, 10069] C303
33) [10301, 1206, 198793] C3 x C303 ---) [4057, 603, 41204] C303
34) [11197, 4001, 2521197] C3 x C303 ---) [5717, 8002, 5923213] C303
35) [11369, 4355, 3237956] C3 x C303 14) [2801, 4883, 1136900] C3 x C303
36) [12269, 4018, 60925] C3 x C303 ---) [2437, 2009, 993789] C303
37) [14969, 4994, 4738109] C3 x C303 ---) [3461, 2497, 374225] C303
38) [15737, 9131, 17062976] C3 x C303 ---) [5441, 7043, 6294800] C303
39) [15773, 5653, 4021] C3 x C303 ---) [4021, 7077, 4558397] C303
40) [17477, 3378, 1105021] C3 x C303 ---) [3061, 1689, 436925] C303
41) [18269, 3401, 475625] C3 x C303 10) [761, 2167, 1169216] C3 x C303
42) [18701, 5125, 4878641] C3 x C303 ---) [5801, 10250, 6751061] C303
43) [18701, 3197, 2513125] C3 x C303 ---) [4021, 6394, 168309] C303
44) [32833, 778, 19989] C3 x C303 ---) [2221, 389, 32833] C303
45) [34253, 209, 2357] C3 x C303 ---) [2357, 418, 34253] C303
46) [38593, 1587, 388436] C3 x C303 ---) [269, 3174, 964825] C303
47) [45641, 1162, 154997] C3 x C303 ---) [293, 581, 45641] C303
48) [88337, 1491, 3664] C3 x C303 3) [229, 2982, 2208425] C3 x C303
49) [89069, 1250, 34349] C3 x C303 ---) [701, 625, 89069] C303
50) [119701, 413, 12717] C3 x C303 ---) [157, 826, 119701] C303
51) [124577, 2447, 1465808] C3 x C303 ---) [317, 4894, 124577] C303
52) [125117, 2830, 353] C3 x C303 ---) [353, 1415, 500468] C303
53) [149921, 911, 170000] C3 x C303 ---) [17, 1643, 599684] C303
54) [169097, 419, 1616] C3 x C303 ---) [101, 838, 169097] C303
55) [228581, 1914, 1525] C3 x C303 ---) [61, 957, 228581] C303
56) [260873, 643, 38144] C3 x C303 ---) [149, 1286, 260873] C303
57) [271253, 581, 16577] C3 x C303 ---) [137, 1162, 271253] C303
58) [318653, 737, 56129] C3 x C303 ---) [41, 1474, 318653] C303
59) [343601, 615, 8656] C3 x C303 9) [541, 1230, 343601] C3 x C303
60) [699437, 849, 5341] C3 x C303 ---) [109, 1698, 699437] C303
61) [805073, 2747, 75088] C3 x C303 ---) [13, 1917, 805073] C303
62) [937721, 1355, 224576] C3 x C303 ---) [29, 2710, 937721] C303
63) [1050013, 1025, 153] C3 x C303 ---) [17, 2050, 1050013] C303
64) [1130081, 1103, 21632] C3 x C303 ---) [8, 2206, 1130081] C303
65) [1378561, 1181, 4050] C3 x C303 ---) [8, 2362, 1378561] C303
66) [1475017, 1795, 436752] C3 x C303 ---) [337, 3590, 1475017] C303
67) [2235377, 4619, 304192] C3 x C303 ---) [97, 9238, 20118393] C303
68) [4306381, 3249, 1562405] C3 x C303 ---) [5, 4157, 4306381] C303
69) [4431961, 2107, 1872] C3 x C303 ---) [13, 4214, 4431961] C303
70) [5255449, 2299, 7488] C3 x C303 ---) [13, 4598, 5255449] C303
71) [5614153, 2371, 1872] C3 x C303 ---) [13, 4742, 5614153] C303
72) [6241009, 2567, 87120] C3 x C303 ---) [5, 5134, 6241009] C303
73) [6471193, 2545, 1458] C3 x C303 ---) [8, 5090, 6471193] C303
74) [7319561, 2819, 156800] C3 x C303 ---) [8, 5638, 7319561] C303
75) [9362153, 3155, 147968] C3 x C303 ---) [8, 6310, 9362153] C303
76) [16421549, 7537, 10096205] C3 x C303 ---) [5, 8401, 16421549] C303
77) [19066841, 4379, 27200] C3 x C303 ---) [17, 8758, 19066841] C303